|I think you are misunderstanding what a DNS is. If the computer is on the same LAN as you are it will have the same DNS address as you have.|
What you are looking for is the IP address of the computer. The easiest way to do that is to go to a command prompt and type ping computer name.
Computer name being the name of the computer you want to know the IP address for. Windows will resolve the IP address for you from the computer name with its built in LAN DNS server.
You can do the same for any computer on the internet that has a URL. Type ping www.computing.net and it will come back the the IP address of this site which just happens to be 220.127.116.11
It was a DNS server somewhere in the big wild world the converted the URL to an IP address.